MinT - Best Known (112−54, 112, s)-Nets in Base 9

Best Known (112−54, 112, s)-Nets in Base 9

(112−54, 112, 232)-Net over F₉ — Constructive and digital

Digital (58, 112, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 56, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(112−54, 112, 253)-Net over F₉ — Digital

Digital (58, 112, 253)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−54, 112, 12390)-Net in Base 9 — Upper bound on s

There is no (58, 112, 12391)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75127 393392 138596 642740 527102 125770 925466 467372 658264 296926 337130 528755 735177 845002 078440 438564 815526 126569 > 9¹¹² [i]